Communication of information using carrier signals having an in-phase component signal and an out-of-phase component signal is well known.
The in-phase component of the two-dimensional carrier signal may be a sinusoid, e.g., cos(ωt), and the out-of-phase component may be a 90 degree phase-shift of the in-phase component, e.g., sin(ωt). Referenced to a complex plane having a “real” and an imaginary or “j” axis, the carrier signal may be represented as cos(ωt)−j sin(ωt), and the in-phase component signal, cos(ωt), may be referenced as the “I” signal, and the out-of-phase component signal may be referenced as the “quadrature” or “Q” signal. Such communication may therefore be referred as “two-dimensional” signaling.
Quadrature-amplitude modulation (QAM) is one example of a two-dimensional signaling. In QAM, symbols, e.g., binary bits or groups of binary bits, are encoded as amplitude-phase states of a transmission signal, each of the states being from a constellation of amplitude-phase states defined on the complex plane by the particular QAM coding scheme. As known, there may be N different ones of the states within the constellation, or different changes of states, representing different symbols.
Illustrative examples of QAM include, but are not limited to, binary phase shift keying (BPSK), which has a two-state constellation, quadrature phase shift keying (QPSK), having a four-state constellation and, more generally, M-ary phase-shift keying, having an M-state constellation.
A typical QAM receiver extracts the symbol sequence from the QAM transmission using a local baseband oscillator, having (within an acceptable accuracy and stability) the same frequency as the oscillator used by the transmitter, and a phase-shift arrangement to generate a local in-phase and quadrature-phase baseband mixing signal.
However, as also known, because QAM encodes information using relative amplitude and phase between I and Q signals, QAM systems are necessarily sensitive to the inaccuracies, e.g., imbalances, occurring within I and Q generation, mixers and propagation paths.